Form-finding of constrained tensegrity structures in the rigid-body space

This paper presents a modified dynamic relaxation (MDR) method for the form-finding of constrained tensegrity structures in the rigid-body space. A screw-theory-based constrained pseudo-dynamic formulation is developed by establishing the kinematic relationships among rigid bodies, nodes, and cables, so that the equilibrium configuration can be solved directly in the rigid-body space. Multiple constraints are incorporated into a unified framework, which extends form-finding analysis from conventional class-1 tensegrity structures in the nodal space to more general class-k systems in the rigid-body space. The proposed method can also accommodate continuous cables. Its effectiveness is verified through three representative examples, together with comparisons against MuJoCo-based dynamic simulation and experimental validation. Therefore, the proposed method provides a unified rigid-body-space formulation for the constrained tensegrity structures considered in this study, and extends form-finding analysis from conventional nodal-space descriptions to rigid-body-based systems involving multiple constraints.